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How to find the cube root of $10$ by Newton-Raphson method correct up to $5$ significant figures?

nmasanta
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Tilak Bhattacharya
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    You choose a function for which $\sqrt[3]{10}$ is a root, make an initial guess as to what that root may be, then apply the method a couple of times. What is stopping you? – Arthur Jun 19 '19 at 07:30
  • Welcome to MSE. Your question is phrased as an isolated problem, without any further information or context. This does not match many users' quality standards, so it may attract downvotes, or be put on hold. To prevent that, please [edit] the question. This will help you recognise and resolve the issues. Concretely: please provide context, and include your work and thoughts on the problem. These changes can help in formulating more appropriate answers. – José Carlos Santos Jun 19 '19 at 07:35

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Start by defining $f(x) = x^3 - 10$. By simple differentiation, $f'(x)=3x^2$.

You want to find the single real zero of $f(x)$.

You can start with an obvious initial estimate of $x_0=2$.

Now apply Newton-Raphson, which iteratively gives $x_{n+1} = x_n - \frac{f(x_n)}{f'(x_n)}$.

Do this until the last significant digit required stops changing.

Deepak
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